There are several lines of evidence that suggest early Mars was warmer and wetter than it is at present. Perhaps the most convincing of these are the valley networks and degraded craters that characterize much of the ancient terrains. In both cases, fluvial activity associated with liquid water is believed to be involved. Thus, Mars appears to have had a warmer climate early in its history than it does today. How much warmer is not clear, but a common perception has been that global mean surface temperatures must have been near freezing - almost 55 K warmer than at present. The most plausible way to increase surface temperatures is through the greenhouse effect, and the most plausible greenhouse gas is CO2. Pollack et al. estimate that in the presence of the faint young Sun, the early Martian atmosphere would have to contain almost 5 bar of CO2 to raise the mean surface temperature up to the freezing level; only 1 bar would be required if the fluvial features were formed near the calculations now appear to be wrong since Kasting showed that CO2 will condense in the atmosphere at these pressures and that this greatly reduces the greenhouse effect of a pure CO2 atmosphere. He suggested that alternative greenhouse gases such as CH4 or NH3, are required. The early Mars dilemma is approached from a slightly different point of view. In particular, a model for the evolution of CO2 on Mars that draws upon published processes that affect such evolution was constructed. Thus, the model accounts for the variation of solar luminosity with time, the greenhouse effect, regolith uptake, polar cap formation, escape, and weathering.